We discuss the \((1+1)\)-dimensional wave maps equation with values in a compact Riemannian manifold . Motivated by the Gibbs measure problem, we consider Brownian paths on the manifold as initial data. Our main theorem is the probabilistic local well-posedness of the associated initial value problem. The analysis in this setting combines analytic, geometric, and probabilistic methods.

中文翻译：

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波图方程和布朗路径

我们讨论具有紧致黎曼流形中的值的\((1+1)\)维波图方程。受吉布斯测度问题的启发，我们将流形上的布朗路径视为初始数据。我们的主要定理是相关初始值问题的概率局部适定性。此设置中的分析结合了解析、几何和概率方法。